Wish me luck,...

as my bike, packed in a standard frame box is in the hands of luggage handling crew of Lufthansa.

No surcharges but they had me sign partial release form on the grounds of inadequate packing
I got the promise of manual handling, hope it makes it through a transfer in Munich.
They seemed to be only concerned about deflating the tires.

Never done the box method, but I've used a soft bike bag many times without incident. The trick is to make sure the sides are layered with an inch or so of foam. Also, for steel frames those dropout holders or old hubs work well to keep the frame in alignment.

Close inspection of the bike revealed two correctible issues:
The tip of the rear axle cut through the box and the axle was squeezed in - now I know how you dissassemble Mack hubs The other thing that cut through was a chainring - one tooth was slightly bent - straightended with no problems.